• Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

image

Play button

image

Play button

image

Progress

1/19

Click to flip

19 Cards in this Set

  • Front
  • Back
The ________ of a matrix is formed by writing its columna as rows.
transpose

examples:
|2|
A =|8|, A^T =[2 8]
A matrix that has only one column is called a _____ matrix or ______ vector.
column, column

[ 2 ]
A = | 3 |
[ 2 ]
FINDING THE INVERSE OF A MATRIX BY GAUSS-JORDAN ELIMINATION
Let A be a square matrix of order n.
1. Write the n*2n matrix that consists of the given matrix A on the left and the n*n identity matrix I on the right to obtain [A : I]. Note that you separate the matrices A and I by a dotted line. This process is called adjoining the matrices A and I.
2. If possible, row reduce A to I using ERO's on the entire matrix [A : I]. The result will be the matrix [I : A^-1]. If this is not possible, then A is not invertible.
3. Check your work by multiplying to see that AA^-1 = I = A^-1*A.
Two matrices A = [aij] and B = [bij] are ________ if they have the same size (m * n) and aij = bij for 1 <= i <= m and 1 <= j <= n.
equal
Properties of Zero Matrices:
If A is an m*n matrix and c is a scalar, then the following properties are true.
1. A + Omn = ?
2. A + (-A) = ?
3. if cA = Omn,, then c = ? or A = ?
1. = A
2. = Omn
3. = 0 or = Omn
A matrix that has only one row is called a ______ matrix or ______ vector.
row, row

A = [2 3 4]
If A is an invertible matrix, then its inverse is ______. The inverse of A is denoted by A^-1.
unique
If A = [aij] and B = [bij] are matrices of size m*n, then their _____ is the m*n matrix given by

A + B = [aij + bij]
sum, The sum of two matrices of different sizes is undefined.

|-1 2| + | 1 3| = |-1+1 2+3| = | 0 5|
| 0 1| |-1 2| | 0-1 1+2| |-1 3|
Find the product AB, where
|-1 3| |-3 2|
A = | 4 -2| and B =|-4 1|
| 5 0|
|-9 1|
|-4 6|
|-15 10|
Real numbers are referred to as ______.
scalars
A matrix that does not have an inverse is called ______ (or _______).
noninvertible
singular
You can use -A to represent the scalar product ______.
(-1)A

A - B = A + (-B)
Properties of Matrix Multiplication
If A, B, and C are matrices (with sizes such that the given matrix products are defined) and c is a scalar, then the following properties are true.
1. A(BC) = ?
2. A(B + C) = ?
3. (A + B)C = ?
4. c(AB) = ?
1. (AB)C (associative property of multiplication)
2. AB + AC (distributive property)
3. AC + BC (distributive property)
4. (cA)B = A(cB)
If A = [aij] is an m*n matrix and B = [bij] is an n*p matrix, then the product AB is an ________ matrix.
m*p

AB = [cij] where

cij = (Summation from k = 1 to n) aik*bkj = ai1*b1j + ai2*b2j +...+ ain*bnj
An n*n matrix A is ______ (or _______) if there exist an n*n matrix B such that
AB = BA = In
where (In) is the identity matrix of order n. The matrix B is called the (multiplicative) _______ of A.
invertible
nonsingular
inverse
If A = [aij] is an m*n matrix and c is a scalar, then the _________ _______ of A by c is the m*n matrix given by
cA = [caij].
scalar multiple
Properties of the Identity Matrix
If A is a matrix of size m*n, then the following properties are true.
1. AIn = ?
2. ImA = ?
1. = A
2. = A
Properties of Transpose
If A and B are matrices (with sizes such that the given matrix operations are defined) and c is a scalar, then the following properties are true.
1. (A^T)^T = ?
2. (A + B)^T = ?
3. (cA)^T = ?
4. (AB)^T = ?
1. A
2. A^T + B^T (transpose of a sum)
3. c(A^T) (transpose of a scalar multiple)
4. B^T*A^T (transpose of a product)
Properties of matrix addition and scalar multiplication:
1. A + B = ?
2. A + (B + C) = ?
3. (cd)A = ?
4. 1A = ?
5. c(A + B) = ?
6. (c + d)A = ?
1. = B + A (commutative property of addition)
2. = (A + B) + C (associative property of addition)
3. = c(dA)
4. = A
5. cA + cB (distributive property)
6. cA + dA (distributive property)